N=16 magicity revealed at the proton drip-line through the study of 35Ca

Abstract

The last proton bound calcium isotope ${}^{35}$Ca has been studied for the first time, using the ${}^{37}$Ca($p,t$)${}^{35}$Ca two neutron transfer reaction. The radioactive ${}^{37}$Ca nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid hydrogen target CRYPTA, to produce tritons $t$ that were detected in the MUST2 detector array, in coincidence with the heavy residues Ca or Ar. The atomic mass of ${}^{35}$Ca and the energy of its first 3/2${}^{+}$ state are reported. A large $N=16$ gap of 4.61(11) MeV is deduced from the mass measurement, which together with other measured properties, makes ${}^{36}$Ca a doubly-magic nucleus. The $N=16$ shell gaps in ${}^{36}$Ca and ${}^{24}$O are of similar amplitude, at both edges of the valley of stability. This feature is discussed in terms of nuclear forces involved, within state-of-the-art shell model calculations. Even though the global agreement with data is quite convincing, the calculations underestimate the size of the $N=16$ gap in 36Ca by 840(110) keV.